Inference for causal interactions for continuous exposures under dichotomization

Dichotomization of continuous exposure variables is a common practice in medical and epidemiological research. The practice has been cautioned against on the grounds of efficiency and bias. Here we consider the consequences of dichotomization of a continuous covariate for the study of interactions. We show that when a continuous exposure has been dichotomized certain inferences concerning causal interactions can be drawn with regard to the original continuous exposure scale. Within the context of interaction analyses, dichotomization and the use of the results in this article can furthermore help prevent incorrect conclusions about the presence of interactions that result simply from erroneous modeling of the exposure variables. By considering different dichotomization points one can gain considerable insight concerning the presence of causal interaction between exposures at different levels. The results in this article are applied to a study of the interactive effects between smoking and arsenic exposure from well water in producing skin lesions.